BUS 232

Two groups. A real difference?

Name: Business Tutor
Address: Burnaby, BC, CA
Telephone: +1-604-916-5838
Price range: C$30–C$129

Compare means, matched pairs and proportions. Choose the right test, measure the uncertainty, and explain what the evidence says.

Independent means · known spread · Step 1 of 22

Start with how the data were collected

Design	What to compare
Unrelated groups; known σ	Difference of means → z
Unrelated groups; equal unknown variances	Difference of means → pooled t
Unrelated groups; unequal unknown variances	Difference of means → Welch t
Matched observations	Within-pair differences → paired t
Yes/no in two groups	Difference of proportions → z

Highlighted row: chosen design

Independent means · known spread · Step 1 of 22

Start with how the data were collected

We compare two population means or two proportions. Independent samples contain unrelated observations across the groups. Paired samples connect each first observation to one second observation, often the same person before and after. Having equal sample sizes alone does not create pairs.

Try it: Switch between unrelated groups and the same people measured twice.

How were observations collected?

Choose the method from the design and assumptions before looking at the p-value.

Check yourself

Two different classes each have 25 students. Are their test scores automatically paired?

Question 1 of 10CoreTutorial question from the slides

Food spending: known sigma

Group 1 is Chicago; group 2 is New York. Independent random samples of baseball fans have mean food spending $13.60 (n = 40) and $14.75 (n = 36). Known population SDs are $1.80 and $2.50. Test whether the true difference differs from $0.00. State the hypotheses, find the standard error, test statistic, critical value and p-value, and conclude at α = 5.00%.

Given

Independent samples

	Group 1	Group 2
Sample mean	13.60	14.75
Population σ	1.80	2.50
Sample size	40	36

Null difference, Δ₀0

Significance, α5%

Solution

The null model: reveal the p-value to shade its tail

Mean = 0

Probabilities include the full tails beyond the visible curve.

Read the question and the givens first. Try the first part yourself, then press Start solving and open the working to check.

Standard error

Test statistic

Critical value

p-value

Decision

Two-sample tests still feel hard to tell apart?

Bring your problem sets. We work through them together until every type feels routine.

Book a session Next toolNext: Correlation, simple regression and reading multiple regression output

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Two groups. A real difference?

Start with how the data were collected

Start with how the data were collected

Food spending: known sigma

Two-sample tests still feel hard to tell apart?

Questions, answered.

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